If you're a foreign national and you're here legally, you have something called a green card or a VISA or a stamp on your passport.
The Matricula Consular is a card issued by foreign governments, not just Mexico, although in this case they're of primary concern.
Many of the Mexican officials have talked about this Matricula card openly and stated that it was their way of getting around the Amnesty problem.
We should never, ever, use some foreign government's card to determine whether someone has legal status here in the United States.